Answer the following questions,which help you understand the difference between Thomson's model and Rutherford's model better.
$(a)$ Is the average angle of deflection of $\alpha$-particles by a thin gold foil predicted by Thomson's model much less,about the same,or much greater than that predicted by Rutherford's model?
$(b)$ Is the probability of backward scattering (i.e.,scattering of $\alpha$-particles at angles greater than $90^{\circ}$) predicted by Thomson's model much less,about the same,or much greater than that predicted by Rutherford's model?
$(c)$ Keeping other factors fixed,it is found experimentally that for small thickness $t$,the number of $\alpha$-particles scattered at moderate angles is proportional to $t$. What clue does this linear dependence on $t$ provide?
$(d)$ In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of scattering of $\alpha$-particles by a thin foil?

(A-D) About the same.
The average angle of deflection of $\alpha$-particles by a thin gold foil predicted by Thomson's model is about the same as that predicted by Rutherford's model because the average angle is a macroscopic result of many small interactions in both models.
$(b)$ Much less.
The probability of backward scattering (scattering at angles $> 90^{\circ}$) predicted by Thomson's model is much less than that predicted by Rutherford's model,as Thomson's model assumes a uniform distribution of positive charge,preventing large-angle deflections.
$(c)$ Scattering is mainly due to single collisions.
The linear dependence on thickness $t$ suggests that the scattering is primarily the result of single collisions with individual atoms. As the number of target atoms increases linearly with thickness,the probability of a single collision also increases linearly.
$(d)$ Thomson's model.
It is wrong to ignore multiple scattering in Thomson's model because a single collision in this model causes very little deflection. Therefore,the observed average scattering angle can only be explained by the cumulative effect of multiple scattering events.